A Mathematical Model for Managing Renewable Energy Fluctuations and Automated Battery Activation - final version

this note presents a mathematical framework for real-time wave stability monitoring and automated battery activation in electrical grids to mitigate renewable energy fluctuations. By establishing a scale-invariant stability index, derived from exponential growth derivatives and adapted for sinusoidal waves, the methodology isolates system dynamics from external amplitude and nominal frequency variations. To ensure bounded real-time execution and reduce computational latency in embedded processors, pre-calculated values of the index are mapped across the full 2π radian cycle into a Look-Up Table (LUT), enabling conditional-free phase unwrapping. The control architecture integrates a processing pipeline featuring a Kalman Filter and embedded time-duration thresholds to filter out transient grid noise and prevent false tripping. Mathematical and algebraic validation demonstrates that the framework provides a solution for autonomous energy storage integration during structural grid faults.